Sure, and three days is pretty slim - its easy to be pretty sick for three days with a single occurrence of illness. But the above quote is just a wordy way of saying "you aren't entitled to more sick leave than the 3 days provided for by this law".

Federal law [0] says you cant be fired for taking up to 12 weeks off per year to take care of, among other things, "major illness" (understood to mean that it does not cover things like colds or flu, unless they require hospitalization). But, it also only applies to businesses with over 50 employees, so non-chain restaurants are unlikely to follow this law.

[0] https://en.wikipedia.org/wiki/Family_and_Medical_Leave_Act_o...